Spatial agglomeration and endogenous growth

This paper constructs a dynamic general equilibrium model with spatial interactions in which a human capital externality is the centripetal force towards agglomeration. The resource cost of transportation is, on the other hand, the main centrifugal force, preventing a city from growing unboundedly. A central feature of our analysis is the dynamic interaction between (perpetual) economic growth and (bounded) city growth. We examine the socially optimal and the decentralized growth rates as well as city sizes. In the decentralized environment, individuals under-invest, whereas cities are under-populated. We show how public policies may enable a decentralized city to attain the socially optimal allocation.     

Spatial externalities and agglomeration in a competitive industry

We introduce spatial spillovers as an externality in the production function of competitive firms operating within a finite spatial domain under adjustment costs. Spillovers may attenuate with distance and the overall externality could contain positive and negative components with the overall effect being positive. We show that when the spatial externality is not internalized by firms, spatial agglomerations may emerge endogenously in a competitive equilibrium. The result does not require increasing returns at the private or the social level, increasing marginal productivity of private capital with respect to the externality, or location advantages. In fact agglomerations may emerge with decreasing returns to scale, declining marginal productivity of private capital with respect to the externality, and no location advantage. The result depends on the interactions between the structures of production technology and spatial effects as shown in the paper. No agglomerations emerge at the social optimum when spillovers are internalized and diminishing returns both from the private and the social point of view prevail. Numerical experiments with Cobb–Douglas and CES technologies and an isoelastic demand confirm our theoretical predictions.     

Can industrial agglomeration achieve the emission-reduction effect?

This paper adopted the Meta-constraints efficiency model to measure the environmental efficiency of the industry in China, and then used the spatial panel model to analyze the impact of industrial agglomeration externalities on environmental efficiency. The study found that industrial agglomeration exerted an apparent spatial spillover effect. Different agglomeration degrees and means may be matched with different environmental effects. With the evolution of agglomeration, the balanced effects among negative externality of scale (pollution effect). Marshallian and Jacobs positive externality (self-purification effect) lead to a U-curved tendency between industrial agglomeration and environmental efficiency. Therefore, with the increase of industrial agglomeration degree, the environmental efficiency first decreases and then increases. The effect of industrial agglomeration in the Midwest on the environment is mainly presented as a negative externality of scale, situated in the descending phase of the U curve. However, the effect of eastern industrial agglomeration on the environment mainly manifested as Marshallian and Jacobs positive externalities and was situated close to the ascending phase of the U curve. All regions should fully utilize the “self-purification” effect of the Marshallian externality and the Jacobs externality on emission-reduction according to the different phases of industrial development.     

A note on tax competition in the presence of agglomeration economies

This paper analyzes tax competition in the presence of agglomeration effects. The obtained results are then compared to the results of the traditional model, without agglomeration effects. As is well known, the presence of a fiscal externality affects the provision of the public good in the standard competitive model of tax competition. In the model with agglomeration effects, in addition to this externality, a new effect shows up. This effect reflects heightened government concern about capital flight, which depresses firm productivity by limiting external economies of scale. As a result, capital tax rates end up being lower than in the case where agglomeration effects are not present, worsening the underprovision of the public good. This conclusion holds in both the competitive and strategic versions of the model.     

Optimal investment with vintage capital: Equilibrium distributions

The paper concerns the study of equilibrium points, or steady states, of economic systems arising in modeling optimal investment with vintage capital, namely, systems where all key variables (capitals, investments, prices) are indexed not only by time but also by age. Capital accumulation is hence described as a partial differential equation (briefly, PDE), and equilibrium points are in fact equilibrium distributions in the variable of ages. A general method is developed to compute and study equilibrium points of a wide range of infinite dimensional, infinite horizon, optimal control problems. We apply the method to optimal investment with vintage capital, for a variety of data, deriving existence and uniqueness of equilibrium distribution, as well as analytic formulas for optimal controls and trajectories in the long run. The examples suggest that the same method can be applied to other economic problems displaying heterogeneity. This shows how effective the theoretical machinery of optimal control in infinite dimension is in computing explicitly equilibrium distributions. To this extent, the results of this work constitute a first crucial step towards a thorough understanding of the behavior of optimal paths in the long run.     

On the smoothness of optimal paths II: some local turnpike results

We study the local turnpike property for two classes of infinite-horizon discrete-time deterministic maximization problems which have common applications, e.g., optimal growth theory. We follow a functional-analytic approach and rely on an implicit function theorem for the space of the sequences which converge to zero. We shall assume the existence of an optimal path which is not necessarily a steady-state. Relying on material developped in Blot and Crettez (Decis Econo Finance 27:1–34, 2004), “On the smoothness of optimal paths” Decis Econ Finance, 21:1–34, 2004), we provide conditions under which a variation in the initial conditions (i.e., capital stock and discount rate) yields an optimal solution which converges toward a reference solution when time becomes infinite. We also provide new results on bounded solutions of difference equations. We gratefully thank the editor, Silvano Holzer, and two anonymous referees for remarks and advices on a previous version of this paper.     

工业劳动力流动、技术溢出与经济地理新均衡——新经济地理学基础模型新发展

在原始核心边缘模型基础上发展的新的核心边缘模型假设工业工人的劳动生产率不再是外生变量,而是跟产业集聚的外部性有关。发展的核心边缘模型不仅验证了原始核心边缘模型的基本性质,还得到了一些新的结论：第一,工业企业生产规模报酬递增程度高有利于产业的集聚,但工业企业生产的规模报酬递增程度低也会诱发产业的重新集聚。第二,产业的空间分布受两股相反力量（集聚力和分散力）的支配。一般情况下,本地市场效应和生活成本效应是促进工业企业集聚的力量,市场拥挤效应则是促使工业企业走向分散布局的力量。第三,在加入本地与跨界技术溢出效应后,对称结构稳定的贸易自由度范围缩小了,而核心边缘结构稳定的贸易自由度范围扩大了。     

Location, innovation and trade: The role of localization and nation-based externalities

This paper models locales that produce goods for trade outside their boundaries. We use a model that assumes monopolistic competition in both service and traded goods sectors; and, influenced by Porter (The Competitive Advantage of Nations, The Free Press, New York, 1990), we study the impact of both a localization externality and a nation-based externality. The localization externality is related to innovation that occurs because of agglomeration in the locale. The nation-based externality reflects the idea that some nations promote competitive industries more successfully than do others. We identify two types of comparative statics effects related to two distinct results of innovation.     

Optimal investment models with vintage capital: Dynamic programming approach

The dynamic programming approach for a family of optimal investment models with vintage capital is here developed. The problem falls into the class of infinite horizon optimal control problems of PDE’s with age structure that have been studied in various papers (12, 11, 33 and 35) either in cases when explicit solutions can be found or using Maximum Principle techniques.     

The intrinsic comparative dynamics of locally differentiable feedback Nash equilibria of autonomous and exponentially discounted infinite horizon differential games

The comparative dynamics of locally differentiable feedback Nash equilibria are derived for the ubiquitous class of autonomous and exponentially discounted infinite horizon differential games. The resulting refutable implications are intrinsic to the said class of differential games, and thus form their basic, empirically testable, properties. Their relationship with extant results in the optimal control theory and the static game theory is discussed. Separability conditions are identified on the instantaneous payoff and transition functions under which the intrinsic comparative dynamics collapse, in form, to those in optimal control problems. Applications of the results to capital accumulation and sticky-price games are provided.     

Feasibility and optimality of the initial capital stock in the Ramsey vintage capital model

Using a discrete-time version of the Ramsey Vintage Capital Model we provide a characterization of the set of initial capital stocks compatible with a predefined scrapping time, given the rate of technical progress and the level of capital productivity. Each profile of initial capital stock in that set generates a complete infinite horizon feasible capital path. From that characterization, we prove the existence of a minimum value for the scrapping time of the machines compatible with the rate of technological progress. Moreover, for each level of capital productivity, there exists an upper bound for the technological progress which allows the existence of feasible capital paths with full employment. Finally, we transform the infinite horizon dynamic programming problem into one of finite dimension. We use this to find the optimal lifetime for the machines as well as the optimal composition of the initial capital stocks. A numerical example shows that, in accordance with the infinite horizon approach to the problem, the increase in the rate of technological progress leads to a decrease in optimal scrapping time of capital goods.     

浦东新区极化开发的负社会外部性研究

当前中国正处于工业化和城市化加速发展时期,城市规模和数量在不断增长,对于城市未来和城市居民福利的关注,已经使人们在最近几年对于城市问题引发了许多的关注.过去人们只关注于极化开发的经济功能,而忽视极化开发造成人口大量流入、快速城市化造成的城市社会结构和城市功能结构转变引发的负社会外部性问题.本文探索了极化开发造成负社会外部性的机理,并利用人口普查资料及其它社会经济统计资料,分析浦东新区极化开发的集聚效应和负社会外部性.当前浦东新区极化开发引发的负外部性问题如社会极化、社区重组、社会隔离、就业压力已经开始显现,并对浦东新区的社会稳定和可持续发展产生一定的影响.浦东新区极化开发产生的负社会外部性问题在中国其它许多大城市也开始凸显,因此,如何最大限度地减少极化开发的负社会外部性问题应引起重视.     

The effects of agglomeration externalities on urban green total-factor productivity in China

For China's urban industrial layout and green development, determining which types of agglomeration externalities are most advantageous to the rise of green total-factor productivity has both theoretical and practical relevance. This research experimentally studies the effects of three types of agglomeration externalities on urban green total-factor productivity using the data of 285 Chinese cities from 2003 to 2018. The findings demonstrate that urban green total-factor output is rising, albeit with certain differences during different time periods. Both the Jacobs externality and the Porter externality are favorable for increasing urban green total-factor production when all cities are evaluated together, although the latter has a stronger promoting influence. The effect of the Marshall-Arrow-Romer externality, on the other hand, is not significant. Furthermore, these effects also depend on the stage of economic development and population size.     

Integration, agglomeration and welfare

This paper studies the social desirability of agglomeration, and the efficiency arguments for policy intervention in a simple, analytically tractable new economic geography model. The location pattern emerging as market equilibrium is ‘bubble-shaped’, i.e. it features dispersion both at high and low trade costs and stable equilibria with partial and full agglomeration for intermediate levels of trade costs. We show that the market equilibrium is characterized by over-agglomeration for high trade costs and under-agglomeration for low trade costs, and we work out analytically that a net pecuniary externality is the underlying cause of this market failure. One particularly noteworthy result is that the net pecuniary externality is positive at high levels of trade freeness. However, there is no market under-agglomeration unless this positive net pecuniary externality interacts with an additional congestion force originating in the (per se efficient) competitive housing market.     

Externalities in a life cycle model with endogenous survival

We study socially vs individually optimal life cycle allocations of consumption and health, when individual health care curbs own mortality but also has a spillover effect on other persons’ survival. Such spillovers arise, for instance, when health care activity at aggregate level triggers improvements in treatment through learning-by-doing (positive externality) or a deterioration in the quality of care through congestion (negative externality). We combine an age-structured optimal control model at population level with a conventional life cycle model to derive the social and private value of life. We then examine how individual incentives deviate from social incentives and how they can be aligned by way of a transfer scheme. The age-patterns of socially and individually optimal health expenditures and the transfer rate are derived. Numerical analysis illustrates the working of our model.     

Congestion,agglomeration, and the structure of cities

Congestion costs in urban areas are significant and clearly represent a negative externality. Nonetheless, economists also recognize the production advantages of urban density in the form of positive agglomeration externalities. The long-run equilibrium outcomes in economies with multiple correlated but offsetting externalities have yet to be fully explored in the literature. Therefore, I develop a spatial equilibrium model of urban structure that includes both congestion costs and agglomeration externalities. I then estimate the structural parameters of the model using a computational algorithm to match the spatial distribution of employment, population, land use, land rents, and commute times in the data. Policy simulations based on the estimates suggest that congestion pricing may have ambiguous consequences for economic welfare.     

Non‐linear Dynamics in the Infinite Time Horizon Model

Using results from the theory of non‐linear dynamical systems, it has been shown that optimal growth theory can provide new explanations for business cycles and for international differences in growth and development. The present survey concentrates on this aspect of optimal growth theory, that is on the possibility of fluctuations and non‐uniqueness in models of optimal capital accumulation. It is a selective survey on non‐linear dynamics in infinite time horizon models of optimal growth.     

Strategic Location Behaviour: The Case of Japanese Investments in Europe

SUMMARY

We address the question of competition within the location choices of firms. In a framework of agglomeration effects, both spatial and temporal dimensions of the firms' decisions are studied. We show that the competition consequences of preemptive move and optimal time of entry can interfere with the geographical decisions. Our results contrast with those of agglomeration economics models which generally provide extreme results of mono-location. The equilibria described here tend to demonstrate that the relation between competition strength and spatial differentiation remains pertinent in a context of agglomeration economies. A conditional logit empirical study analyses the geographical choice of Japanese firms in Europe. Agglomeration variables, public policies and labour market determinants are tested, highlighting the existence of temporal and spatial proximity in the behaviour of firms. The competition conditions experienced by firms of each specific sector also appear to be important in the location decision of Japanese investors.     

创新空间扩散、集聚租金与经济高质量发展

基于新经济地理学和内生增长理论,构建了一个贸易自由度约束下的局域溢出模型,探究了创新的空间扩散与集聚影响经济高质量发展的作用机制。研究发现：对称均衡是模型的唯一内点均衡;当角点均衡时,存在唯一的贸易自由度支撑区间,此时,如果运输成本变小,则技能劳动力、R&D部门、制造业部门以及创新活动将变得更集聚,同时创新的空间扩散程度变大,外围区域在研发创新方面的劣势减弱;从增长和福利评价的角度看,在技能劳动力存量不变的条件下,创新的空间扩散对整个经济体的经济增长并没有影响,然而,当区域的经济增长源于可流动的技能劳动力集聚时,中心区域的技能劳动力和普通劳动力总是偏好集聚状态,当且仅当创新的空间扩散效应足够大或者集聚租金较小时,外围区域的普通劳动力偏好集聚状态。因此,降低运输成本,提高贸易自由度,有助于增大创新空间扩散效应,减小集聚租金,提高全域劳动力福利水平,从而促进经济的高质量发展。     

Spatial Cournot competition and economic welfare: a note

We investigated welfare implications in location-quantity models in a symmetric linear city. We found that when firms are not agglomerated in equilibrium, increasing the distance between firms raises (reduces) producer surplus and social welfare (consumer surplus). Moreover, central agglomeration is always optimal for consumers among symmetric locations, but not necessarily for producers. Central agglomeration can be inefficient even if it is the unique equilibrium outcome. In short, the firms are more likely to agglomerate or locate closer than what welfare maximizers would dictate, whereas they locate farther apart than what consumer surplus maximizers would recommend.